Reputation general model (RGM) for consolidated entity on liquid market
For purpose of the model let define reputation that it is current or potential cash outflow arising from information not reflected of the current fair value of net assets controlled or influenced by an entity.
Let:
y – represents the fair value of assets controlled or influenced, x – current market value of the equity,
z – value of reputation.
Subject to (initial assumptions):
i. efficient market,
ii. public traded shares of entity on consolidated bases, iii. lack material influences on other companies, iv. net controlled and influenced assets are verifiable,
v. the auditing procedures are efficient, subject to non-material errors, vi. a consolidated values are available.
The following equation denotes the lack of the reputation:
y = x [1]
x ε R; y ε R+
13 P. Staszkiewicz: Ryzyko struktury grupy. In: K. Jajuga & R. Chmielowiec (Eds.). „Inwestycje finansowe i ubezpieczenia – tendencje światowe a rynek polski” 2010, Vol. 183, p. 378.
Model for reputational risk for subsidiaries of non-public group… 55
The equation represents the situation while the fair value of the net con-trolled and influenced assets is equal to the market values. Thus the value of reputation equals
z = x-y [2]
z, x ε R; y ε R+
While 𝑧 ≠ 0 than the reputation is recognized, in any 𝑧 > 0 the reputation assets is build up while for negative values of z there is a fair market expectation that the entity assets include the expected cash outflow due to the reputation.
Let’s denote M as the entity materiality, where M < than the risk appetite of a given entity.
Lemma 1 for |𝑧| ≥ 𝑀 than the reputation risk management system should be in place for any entity. Thus there could be a tendency for high positive z (above M) to set up the risk management system but without recognition the risk value in the risk reporting.
The reputation risk is thus the chance that the z < 0.
For any z < 0 where |𝑧| ≥ 𝑀 the reputation risk should be disclosed by the application true and fair concept of the financial reporting.
The reputation risk value is therefore the value of zk subject to condition that the value is negative. Metric for reputation risk value could be expressed into two timing aspects a spot value of the reputation risk and a long term values for the reputation risk. As the reputation is an attribute of the operational risk measured at the yearly interval the assessment of the spot values of the reputa-tion risk can be ignored (A long-term value assumpreputa-tion 1).
Subject to the lack of efficient market than the x is approximated by the equation:
x = y + z [3]
While y is approximated by fairly audited carrying value of:
a. the consolidated net assets, subject to widely recognized accounting standard (based on fair values) or (Group assumption 2)
b. the unconsolidated net assets, subject to widely recognized accounting stan-dard (based on fair values) (Solo-basis assumption 3).
But the potential outflow due to reputation is derived from different factors not included in the balance sheet position like among others as:
a) Values of the potential customers.
b) Long term costs of publicity of the entity name [denotes as P].
c) Market shares (influences).
Piotr Staszkiewicz 56
d) Incurred but not recognized claims on assets and liabilities [denotes as C].
e) Realized losses on uncontrolled related parties and entities [denotes as L].
f) Human capital value (innovations, creativities).
g) Liquidity (cash flow average position).
h) Conflicts of interests.
i) Market external factors.
As the factor list is potentially infinitive, each of them have an relative con-tribution to entire value of zk. Having taken working assumption that due to the practical observation number of above stated factors are positively each other correlated, than by a professional judgment the P,C,L are unlikely to be strongly positively correlated. Thus z can be expressed as:
zk = 𝛼𝑃 + 𝛽𝐶 + 𝛾𝐿 + 𝜃 [4]
𝛼, 𝛽, 𝛾 – parameters ε R,
𝜃 – represents any other variables.
Assumption 4 It is assumed that 𝜃 is not significant and P,C,L are measur-able.
The proposed model of z in [4] consists of two section 𝛽𝐶 + 𝛾𝐿 represent-ing internally generated negatives drivers jeopardizrepresent-ing the reputation. 𝛼𝑃 – rep-resenting the external cost (or investments) for maintaining reputation.
Any material zk the value should be disclosed or provided within financial statements or risk disclosure based on the IFRS or BASEL risk management standard.
Due to assumption 1 for economically meaningful values of z; the variables should be proofed against a short term vulnerabilities and economic cycle, there-fore let x and y represents a stable average position through the business cycle (a long term structural reputation) than the equation [2] becomes:
𝑧 = 𝑥̅ − 𝑦 [5]
While dash represents the long term average though the cycle.
The above stated model is subject to the numerous assumption, but practi-cally highly demanded are those of the efficient market (market itself), fair con-solidated basis and long term structure.
Model for reputational risk for subsidiaries of non-public group… 57
Non public market model (NPM)
As x is not available from the market than based on the [3] by replacing z with zk the market equity and application instead of y the unscosolidated posi-tion of parent company [yuc] than is:
yuc + 𝛼𝑃 + 𝛽𝐶 + 𝛾𝐿 + 𝜃 but a according to [1] for non material reputation value the fraction:
should be 𝛼𝑃 + 𝛽𝐶 + 𝛾𝐿 + 𝜃 = 0 than unrealized losses of the related par-ties and transaction which does not constitute the reputation risk is equal to:
𝐿 = −𝛾 (𝛼𝑃 + 𝛽𝐶 + 𝜃) [6]
Subject to lack of significant 𝐶 𝑎𝑛𝑑 𝜃 [assumption 5] the simplified test for the existence of the reputation risk holds true:
𝐿 = − 𝑃 [7]
and
𝑃 = 𝐿 [8]
Let us call the equation [8] as simplified tests for lack of the reputation risk (the ”lack test”). Then by applying the assumption 3,4,5 and approximation of L by the net equity of the controlled subsidiary, a case while both all subsidiaries express positive equity and a parent company does not perform reputation related expenditures indicates lack of reputation risk. Thus the parameter is than approximated by the level of the control of over subsidiary assets by parent company.
If any given group consists of companies A and B. A is the parent company owning e.g. 80% share of company B (subsidiary) (ra = 80%), B has a contrapart shareholding in A of 20% (rb = 20%). The shares are expressing, in general, the percentage share ownership of the votes (control) in the shareholder meeting.
Than the effective control rate (ref) would be:
ref =ra -rarb/(1- rarb) [9]
Proof for [9] delivered by Staszkiewicz14.
14 P. Staszkiewicz: Konsolidacja udziałów wzajemnych. „Rachunkowość” 2001, No. 10, p. 667.
Piotr Staszkiewicz 58
In case of the reciprocal holdings, parameters becomes an effective con-trol rate (𝐸𝑓𝑓𝑟) derived from [9], thus the expenditures relating to migrating of the long term reputation risk could represented by:
𝑃 = ∑ 𝐸𝑓𝑓𝑟 ∗ 𝐿 [10]
Where n denotes number of the controlled entities by a parent.
So long the value of P>0 than the reputation risk subject to above assump-tion can be ignored. In case of reputaassump-tion risk averse group the weight 𝑬𝒇𝒇𝒓𝒊 might become 1 for each non positive 𝑳𝒊. The group owner possessed however an reputation option, in case while the realized losses becomes unbearable (exceed the group risk appetite) the subsidiaries can be let bankrupt (appetite or materiality option).
Let us assume (assumption 5) that the risk appetite is expressed as the % of the economic capital, thus the materiality can be expresses as well as the % of the economic capital. Thus the P values between materiality and risk appetite is disclosed with parent company risk profile. Any insignificant values of P can be reasonable ignored while the values exceeding the risk appetite indicate realiza-tion of the reputarealiza-tion oprealiza-tion.
Conclusion
The above presented model allows for quantification of the financial as-pects of reputation. There is a possibility for the practical application of the model, however the added value in contrast to the consolidation procedures quality might not necessary outweigh the costs of application.
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MODEL RYZYKA REPUTACJI PODMIOTU ZALEŻNEGO W SYTUACJI KONTROLI WZAJEMNEJ W NIEPUBLICZNEJ GRUPIE KAPITAŁOWEJ
Streszczenie
Referat przedstawia szkic koncepcyjny modelu do analizy ryzyka reputacji w sytu-acji rynku niepublicznego, w przypadku istnienia kontroli wzajemnej między podmiotem dominującym a zależnym. Został przedstawiony uproszczony test braku ryzyka reputa-cji. Model podstawowy wyprowadzono z zasady ekwiwalencji wartości aktywów i braku wartości dodanej zorganizowanej struktury.